The infinity-categorical structure conjecture for HOM-simplicial sets of $\Omega B As$-algebras

Given two $\Omega B As$-algebras $A$ and $B$, define the HOM-simplicial set by

$$\mathrm{HOM}_{\mathsf{\Omega B As\text{-}Alg}}(A,B)_n:= \mathrm{Hom}_{\mathsf{(\Omega B As,\Omega B As)\text{-}op.\ bimod.}}(n\text{-}\Omega B As\text{-}\mathrm{Morph},\mathrm{Hom}(A,B)).$$

The infinity-categorical structure conjecture. The simplicial sets $\mathrm{HOM}_{\mathsf{\Omega B As\text{-}Alg}}(A,B)_\bullet$ are $\infty$-categories.

This conjecture proposes that the simplicial mapping objects between $\Omega B As$-algebras carry the structure of infinity-categories, extending the higher-algebraic framework developed for these algebras. The supplied text gives no resolution status.